**Normal Distribution**

In most of the natural-procedures, random alterations adapts to specific probability distribution which is called as** normal distribution. **Normal distribution is that probability distribution which is observed commonly by everyone. In the year 1700, mathematicians Laplace and de Moivre used normal distribution. Karl Gauss, a German physicist and mathematician used this distribution for analyzing data of astronomy. Thus, for this reason normal distribution was called as **Gaussian distribution** became more common among many communities of science.

Another definition of normal distribution is that it is a function of statistics which represents random-variable’s distribution in the form of a symmetrical graph having the shape of a bell.

A normal distribution is having a shape similar to the bell, and for this reason it is also sometimes called as** bell curve**. One e.g. of bell curve is given below:

The curve drawn above represent the graph for a given data which is having a **mean of “0” (zero)**. Normal distribution-curve can also be described with the help of following equation of probability density: -

**Characteristics of Bell Curve**

Following are the characteristics of bell curve:

- Symmetric
- Extends to - / + infinity
- Unimodal
- Area which is below the curve is equal to 1.

**Parameters **

We can specify Normal distribution by 2 parameters mentioned below:

- Standard-deviation
- Mean

In the theory of probability, **Gaussian or normal distribution **has been defined as common probability-distribution which is used often as 1^{st} approximation for describing

In the statistics, normal distribution has been considered as the most common probability distribution. This is due to many **reasons** which are mentioned below:

- 1
^{st}, normal distribution are very amenable analytically, i.e., a person can derive large no. of outcomes which involve this normal distribution in an explicit-form. - 2
^{nd}, normal distribution develops in the form of the central-limit-theorem’s outcome, which defines that in a mild situation, sum of big no. of the random-variables is spread normally in an approximate manner. - Finally, normal distribution’s bell-shape makes the distribution convenient option for simulating or modeling random-variable’s huge variety, which is coming across a practice.

**Applications of Normal Distribution**

There are many applications of normal distribution in various fields of a business enterprise. Some of the examples are mentioned below:

- It is generally assumed by the theory of modern-portfolio that the diversified portfolio of asset’s returns follows normal distribution.
- Procedure variations in the operations-management are often normally distributed.
- In HR management, the performance of an employee is sometimes normally distributed.

Normal distribution is often used for describing random-variables, particularly those which have symmetrical-unimodal-distributions. In most of the cases, normal distribution, however, is just a rough idea of actual-distribution. Normal distribution is practiced in many fields such as statistics, social science & natural-science.

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